Pozdnyakov, VladimirSteele, John M2023-05-232023-05-232013-11-012016-09-13https://repository.upenn.edu/handle/20.500.14332/42223We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for permuted sequences of real numbers. Some of these inequalities are new and some are variations of classical inequalities like those introduced by A. Garsia in the study of rearrangement of orthogonal series.© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Construction of martingalespermutation inequalitiesgarsia inequalitycombinatorial martingales; Discrete Brownian bridgeOther MathematicsSet TheoryArticle